CN116209879A

CN116209879A - Method for calibrating a vibrating inertial sensor

Info

Publication number: CN116209879A
Application number: CN202180059263.8A
Authority: CN
Inventors: N·韦尔西尔; B·肖梅; B·莱维里尔
Original assignee: Thales SA
Current assignee: Thales SA
Priority date: 2020-07-24
Filing date: 2021-06-18
Publication date: 2023-06-02
Also published as: US20230251107A1; FR3112850B1; FR3112850A1; WO2022017699A1; EP4185841A1

Abstract

A method (100) for calibrating an inertial angle sensor (10), comprising the steps of: a, at least two electrical angles (θj) for the vibration wave: a1, a sinusoidal stiffness disturbance PSi having a disturbance frequency fi is applied via each of the three trim controls CTi, and for each applied disturbance: a11, determining and storing an estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi based on the excitation control determined by the driver; b, determining three 2 x 2 matrices M 'i from the three estimated excitation forces fei=1, 2, 3 stored in step a11, the matrices M' i representing the responses of the gyrometer to the disturbances PSi; c, determining and storing an estimated inverse excitation matrix (formula (a)) and an estimated inverse detection matrix (formula B) from the three matrices M' i determined in step B, the excitation matrix E and the detection matrix D representing the effect of the excitation chain and the effect of the detection chain of the sensor, respectively.

Description

Method for calibrating a vibrating inertial sensor

Technical Field

The field of the invention is that of vibrating inertial sensors in which two masses are vibrated. The invention relates more particularly to inertial sensors of the MEMS type having a planar structure, typically made by micromachining a support wafer.

Background

Tuning fork inertial sensors are known to those skilled in the art. An inertial sensor made of thin planar wafer micromachining is described in document EP2960625, which allows measurement of angular position (gyroscopes) or angular velocity (gyroscopes). The main features of which are reviewed hereinafter.

The fabrication of such micromachined sensors (also referred to as MEMS (microelectromechanical systems) sensors) uses collective micromachining, etching, doping deposition, etc. techniques similar to those used for the fabrication of electronic integrated circuits, allowing for low production costs.

These sensors consist of two vibrating moving masses M1 and M2 (as shown in fig. 1), which are arranged around each other (concentrically) and are excited in the tuning fork mode via one or more excitation transducers in the plane of the wafer (plane xy in the figure). The two masses are suspended from a fixed anchor point a of the wafer by (orthogonal) suspension springs RS. The two masses are coupled together by a stiffening element RC. The objective is to obtain a stiffness along x equal to the stiffness along y by construction, and a zero coupling stiffness between x and y. Useful vibration modes correspond to inverted linear vibrations of the two masses.

The architecture forms a resonant system in which two masses are coupled together by coriolis accelerations. When the gyroscopic tester rotates about a z-axis (called the sensitive axis) perpendicular to the plane xy, the combination of the forced vibration and the angular rotation vector produces a force by the coriolis effect that sets the moving mass to natural vibration perpendicular to the excitation vibration and the sensitive axis; the amplitude of the natural vibration is proportional to the rotational speed. Electronics associated with the sensor calculate the amplitude of vibration in a direction orthogonal to the direction of excitation, regardless of the direction of excitation (assuming known).

The sensor may operate in a gyroscopic test mode: by modifying the excitation, the direction of the natural vibration is kept fixed relative to the housing of the sensor, and then the output information is an image of the necessary energy that has to be applied to the excitation transducer in order to keep the direction of the natural vibration fixed despite the movement of the housing. The measurement of this reaction force provides the angular velocity Ω of the sensor. The sensor may also operate in a gyro mode: the direction of the natural vibration is free and is detected to provide the angular orientation of the sensor.

The overall structure of the resonator is symmetrical about two axes x and y, which define the sensor reference frame, as shown in fig. 2. Axisymmetry is understood to mean that the structure is symmetrical about x and symmetrical about y. As described below, these axes constitute the main direction of the actuator/detector operating along these two axes.

To excite useful vibration modes in any given direction of the plane, the excitation signal is decomposed into two components of corresponding adjusted amplitude, which are applied to the excitation transducer Ex acting in direction x and the excitation transducer Ey acting in direction y, respectively, which transducers are associated with at least one moving mass (the inner mass M1 in fig. 2). Thus, an excitation force is applied to these transducers to generate and sustain a vibration wave: the transducer is able to maintain forced vibration via amplitude control (to counter damping of the MEMS) as well as via precession control (to rotate the wave) in any direction along the plane xy.

The resulting wave motion is detected by combining information collected by at least one pair of detection transducers Dx, dy that acquire the position of the mass during its travel in the sensor reference frame xy (two of each of fig. 2) and are associated with at least one moving mass.

Preferably, as shown in fig. 3, the transducers are implemented on two masses, index 1 corresponding to mass M1 and index 2 corresponding to mass M2. FIGS. 2 and 3 constitute non-limiting examples of arrangements; many other types of arrangements are possible with constraints on creating an axisymmetric system.

The transducer is preferably implemented by electrodes as a interdigitated comb with gap variations. There are fixed combs (the teeth of the fixed combs are fixed to the fixed electrodes of the processed wafer), and moving combs (the teeth of the moving combs are interdigitated with the teeth of the fixed combs, fixed to the moving masses associated with the transducer under consideration).

The excitation is as follows: at the desired vibration frequency (the mechanical resonance frequency of the suspended moving mass, typically on the order of 10 kHz), an excitation force is applied via an alternating voltage between the moving comb and the fixed comb. The resulting motion is perpendicular to the teeth of the comb.

The detection method comprises the following steps: applying a polarizing voltage between the fixed comb and the movable comb; and is characterized in that: the change in charge due to the change in capacity between the fixed comb and the mobile comb caused by the change in the interval between the teeth of the fixed comb and the mobile comb was observed. The measured movement is a movement perpendicular to the teeth of the comb.

The vibrating assembly of masses/springs is characterized by a symmetrical 2 x 2 stiffness matrix, which is called K. For optimal operation of the sensor, it is sought to obtain a final stiffness matrix proportional to the identity matrix. This is not the case due to imperfections in production (see below for details).

The axis x' is called the vibration axis of the wave. The axis defines a reference frame x ' y ' which is perpendicular to x ' in the plane of the MEMS. The axis x ' forms an angle with the axis x called electrical angle θ, and the reference frame x ' y ' is called wave reference frame. It will now be assumed that the wave vibrates along x (x' =x).

The dynamic equation describing the vibrating gyrometer can be reduced to a simple mass model of mass M, whose displacement X, Y is modeled as follows:

m is a mass matrix; for simplicity, hereinafter, this will be considered as a scalar,

a is a damping matrix, K is a stiffness matrix, C is a coriolis matrix and has values:

where M is the mass, and Ω is the angular velocity,

FX and FY are excitation forces applied along axes x and y of the gyroscopic tester. These forces come from demodulation based on displacement of the detected signal relative to vibration, control Cr, ca, cq and Cp in the wave reference frame calculated by servo control known to those skilled in the art (and not described herein). Based on the measurements of the motion of waves X and Y performed in reference frame xy, rotation is applied to transfer into wave reference frame X 'Y', then control is determined (via demodulation of the detected signal), and counter rotation is applied to transfer back into reference frame xy, where an excitation force is applied. Control is determined such that the displacement of the mass (i.e., the vibration wave of the gyroscopic tester) takes a desired form. In general, the desired form is a linear displacement that oscillates in a given direction with respect to the reference frame xy of the gyroscopic tester.

Controlling Cr corresponds to a stiffness force for controlling a natural frequency of the resonator; since the phase is an integral of frequency, cr controls the phase of the wave. Cr is an external force (estimated displacement) applied to the resonator that modifies the frequency of the vibration by slowing or speeding up the vibration as the resonator vibrates, but does not modify the inherent stiffness of the resonator.

The control Ca corresponds to an amplitude force for controlling the amplitude of the wave, and the control Cp corresponds to an advancing force enabling the control of the angular velocity of the wave.

The control Cq corresponds to an orthogonal force for controlling the wave (that is, ensuring the linearity of the wave, or when the desired wave is not linear, it is generally elliptical, and Cq enables control of the minor axis of the ellipse).

It is well known to those skilled in the art that imperfections in the production of the sensor result in errors in the information being transferred as its output. Most of these imperfections need to be compensated for by balancing the gyroscopic tester.

It is known to perform this compensation by locally removing material (e.g. by laser ablation) so as to modify the distribution of mass or stiffness. This process is expensive or even impossible to implement on a gyroscopic tester made of thin silicon wafer micromachined and whose detection and excitation movements lie in the plane of the substrate.

The first type of imperfection underlying the non-uniformity of the stiffness matrix K is the frequency difference between the principal axis of vibration in the plane of the MEMS and the axis perpendicular to the vibration, corresponding to the stiffness matrix of the system in which the stiffness along axis x is different from the stiffness along the y-axis. It is sought to equalize the resonant frequencies along the two axes mentioned above by means of an adjustable electrostatic stiffness. The electrostatic stiffness (referred to as the equilibrium stiffness) is provided by frequency tuned transducers Tx, ty acting in directions x and y (at least one pair of Tx Ty on at least one mass, see fig. 2). The purpose of the equalization stiffness is to equalize the stiffness along the two axes of vibration by reducing the value of the highest stiffness, thereby equalizing the frequencies. The frequency correction is referred to as "fine tuning".

The second type of imperfections results from the mechanical coupling between the axis of vibration and the vertical axis, which forms the basis of the so-called orthogonal offset. It involves a dynamic stiffness anisotropy defect in the assembly of two vibrating masses, resulting in vibration that is no longer linear but elliptical, and corresponds to the presence of non-zero coupling stiffness. A well-known solution from the prior art is to cancel this by applying a (sinusoidal) force F to the system via an excitation transducer. The problem is that the application of this force is not applied correctly at the correct moment (phase error) and in the correct axis (gain error), which results in the application of drift. To avoid applying force F, the term is physically decoupled not by applying force, but by directly changing the stiffness of the resonator via at least one pair of transducers q+ and Q- (2 q+/Q-pairs in fig. 2) as shown in fig. 2. To obey symmetry and "geometric" anisotropy, and for volume reasons, these transducers operating on X and Y are arranged on diagonals. Correction of the quadrature bias is referred to as quadrature "fine tuning". Preferably, the transducers Tx, ty, q+ and Q-are also finger-like interdigitated combs (as shown in fig. 2 and 3), which are controlled by a DC voltage, and are referred to as trimming combs.

Thus, the transducer for quadrature "trimming" modifies the characteristics of the MEMS to eliminate coupling between the two axes of the wave reference frame, and the transducer for frequency "trimming" modifies the characteristics of the MEMS sensor to eliminate frequency differences between the two axes of the wave reference frame. They modify the intrinsic properties of the resonator. In other words, if acting on the trimming voltage, the stiffness of the resonator changes even when it is not vibrating, contrary to the control Cr described above (which is the force that slows down or accelerates the vibration when the resonator vibrates). The fine tuning is performed with the help of a DC or low frequency voltage that modifies the electrostatic stiffness of the sensor, without the need to evaluate the phase of the vibrations, whereas the control Cr is implemented by sending a sinusoidal voltage (at the resonant frequency of the sensor) after the phase of the vibrations has been estimated. Thus, the change in frequency achieved by fine tuning has completely different properties from the change in frequency achieved by controlling Cr.

They are controlled by fine tuning servo controls (known to those skilled in the art) that generate quadrature fine tuning control CTxy, frequency fine tuning control CTx along X, and frequency fine tuning control CTy along Y. The fine tuning control is a DC voltage.

Thus, using the trimming comb, the stiffness matrix K is directly modified with the help of matrix Kt, and the dynamic equation of the gyroscopic tester is:

the comb used to fine tune the frequency along x modifies the stiffness of the resonator by generating a matrix Kt:

the comb used to fine tune the frequency along y modifies the stiffness of the resonator by generating a matrix Kt:

the orthogonal trimming comb modifies the stiffness of the resonator by generating a matrix Kt:

the rigidities Kx, ky and Kxy correspond to the controls CTx, CTy and CTxy (DC voltages) within the gain coefficients. The control CTx, CTy and CTxy is the voltage to modify the stiffness Kx, ky and Kxy by the comb. By converting K to K-Kt, applying fine tuning control corresponds to modifying the matrix K in differential equation (2).

Fig. 4 illustrates the operation of an inertial sensor according to the prior art. The resonator Res includes the various transducers described above and symbolized by Et (excitation), dt (detection), TQ (quadrature trimming) and TF (frequency trimming). The vibration wave OV vibrates along X' with an electrical angle θ. The processing unit UT takes over the various calculations for servo control and generates for correction the set of control/forces mentioned above in relation to the various transducers. The excitation and fine tuning controls are determined by different servo controls.

In the processing unit, the detected movements X and Y are first converted by rotation through θ into a wave reference frame X 'Y' and then the excitation control is determined in the form of voltages Ux 'and Uy' in the wave reference frame by servo control.

Ux’＝iCa+Cr

Uy’＝iCp+Cq

The fine control is also determined by dedicated servo control.

Control is then switched back to reference frame xy by reverse rotation and then applied (within the gain factor) to the various transducers.

The excitation chain corresponds to the electronics and actuators, enabling the forces calculated by the servo control to be applied to the excitation transducer. Which takes as inputs the forces FXe and FYe estimated by the servo control and provides as outputs the forces FX and FY actually applied to the resonator. The excitation matrix E representing the effect of the excitation chain is defined (see also fig. 5):

where E is the excitation matrix.

There are in fact two types of problems: (1) The fact that the force applied along x looks as if it were along the y-axis (and vice versa): this involves off-diagonal terms E12 and E21. (2) the fact that the forces applied along x and y do not have the same gain: this is related to the fact that E11 is generally different from E22.

The ideal excitation matrix E has the following form:

where E11 is the actual gain.

The detection chain corresponds to the electronic device and the sensor so that it can detect the displacements X and Y of the vibration wave. Which takes as input the actual displacements X and Y and provides as output the estimated displacements Xe and Ye. The detection matrix D representing the effect of the detection chain is defined as (see also fig. 5):

Where D is the detection matrix.

The ideal detection matrix D has the following form:

where D11 is the actual gain.

Fig. 6 shows the effects of the excitation and detection chains using dashed and solid lines, respectively. In terms of actuation, the values of the forces FXe and FYe to be applied are calculated by the servo control Ass of the processing unit. The values actually applied to the resonator are FX and FY due to the excitation chain. Likewise, the true values of displacements X and Y are converted by the detection chain, and Xe and Ye are injected at the input of the servo control Ass. Errors in detection and excitation produce drift errors, and in particular average drift errors that cannot be compensated by means of electrical rotation.

To correct these errors, i.e. to take over the calibration of the sensor, the solution is to determine the inverse matrices inv (E) and inv (D) (or E ^-1 And D ^-1 ) So that a corresponding inverse matrix can be applied to each chain. For ideal correction, the correct value to be applied to the resonator and the correct detection value are obtained, as shown in fig. 7. Fig. 8 shows the operation of the ideal calibration of the sensor. Before inv (E) and inv (D) are injected into the servo control, inv (E) is applied at the output of the servo control Ass and inv (D) is applied to the measurement at the detected output. Then, for ideal correction, there are FXe =fx and FYe =fy, and xe=x and ye=y.

Document US9927256 describes a calibration method enabling it to determine the correction of at least one excitation control applied to a gyroscopic tester: amplitude (control Ca),

Phase (control Cr), angle θ (control Cp), b quadrature (control Cq).

The method comprises the following steps: transmitting a sinusoidal force (which perturbs the gyroscopic tester) at a frequency close to the resonant frequency of the vibration sensor of the sensor, and in that: the detected output is used to extract the excitation error and the detection error therefrom by assuming that the detection signal has the same sinusoidal component as the sinusoidal component of the disturbance in the forced approach. Because the system is linear, the detected signal is used to extract matrices a and B by using the fact that the detected signal has the same frequency characteristics as the inserted disturbance. These matrices a and B are then inserted into the servo control and the method is iterated to reach the predefined criteria. However, other than the general principle, a method for determining coefficients of the matrices a and B is not described, and their roles in correction are not explained. The spirit of this method is to send specific excitation controls and observe what happens in the detection signal. The transmission of force on the excitation control changes the waveform. Not all coefficients of matrices a and B can be observed (determined) by a set of observations provided by excitation control, since observations made in the detection signal exhibit many redundancies with respect to each other, so that some coefficients of a and B are not observable even though the number of equations appears to be sufficient relative to the number of unknowns in the system.

The object of the present invention is to correct the drawbacks by proposing an alternative calibration method that allows to determine the inverse detection matrix and the inverse excitation matrix simultaneously by direct matrix calculation, wherein all the terms of the matrix are observable.

Disclosure of Invention

The subject of the invention is a method for calibrating an inertial angle sensor, comprising:

a resonator having a planar structure symmetrical about two perpendicular axes x and y, a sensor reference frame xy being defined between the two perpendicular axes x and y, and comprising two vibrating moving masses arranged around each other and configured to vibrate in anti-phase at a vibration frequency (ω) and in a direction x 'defining a wave reference frame x' y ', a vibration wave along x' forming an electrical angle with respect to the axis x,

the resonator further comprises a plurality of electrostatic transducers controlled by a voltage and operating on at least one of the two masses along at least one of the two axes x or y,

a pair of detection transducers configured to detect movement of the vibration wave along x and y, and a pair of excitation transducers; based on the detected motion, applying excitation forces in x and y directions to the pair of excitation transducers, respectively, via a plurality of excitation controls determined by servo control, and the pair of excitation transducers for maintaining a vibration wave in a desired form and vibrating in x', and

A pair of transducers for compensating for quadrature bias and a pair of frequency adjustment transducers, the pair of transducers for compensating for quadrature bias being controlled via quadrature control CTxy; the pair of frequency tuned transducers is controlled via a frequency control CTx along x and a frequency control CTy along y, respectively, the three controls CTx, CTy and CTxy being referred to as fine tuning control CTi indexed with i, where i=1, 2, 3.

The method is applied while the sensor is operating according to a gyroscopic test mode and comprises the steps of:

a, for at least two electrical angles of the vibration wave:

a1, sequentially applying a sinusoidal stiffness disturbance PSi having a disturbance frequency fi via each of the three trim controls CTi, and for each applied disturbance:

a11, based on the excitation control determined by the servo control, determining and storing an estimated excitation force Fei to be applied to the resonator in the case of the disturbance PSi,

b, determining three 2 x 2 matrices M 'i from said electrical angles and applied disturbances based on said three estimated excitation forces fei=1, 2, 3 stored in step a11, the matrix M' i representing the response of the gyroscopic tester to the disturbances PSi,

c, determining and storing an estimated inverse excitation matrix based on the three matrices M' i determined in step B

And an estimated inverse detection matrix->

The excitation matrix E and the detection matrix D represent the effect of the excitation chain and the effect of the detection chain of the sensor, respectively.

According to one embodiment, each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to standard servo control of the sensor and an estimated disturbance-compensated excitation force Fepi,

and wherein step B comprises the sub-steps of:

b1) demodulating each estimated excitation force Fei with a vibration frequency and then with an associated disturbance frequency fi to obtain the amplitude of the disturbance compensated excitation force Fepi,

b2, determining a matrix M' i based on the magnitude of the force Fepi.

According to one embodiment, step a is performed with a plurality of electrical angles, and then the matrix M' i is determined in step B by statistically filtering the contribution of the noise of the sensor to the minimization.

According to one embodiment, each representative matrix M' i determined in step B has the following form:

mi is defined by:

and +.>

According to one embodiment, a matrix

And->

Is considered to be close to the unitary matrix and is expressed as:

then, in the case of neglecting the second order term, the three representative matrices M' i determined in step B are represented as:

M’i＝AMi+MiB

And wherein step C comprises the sub-step of determining said matrices a and B based on said matrix M' i.

Preferably, the disturbance frequencies fi i=1, 2, 3 are between less than 1000 times and less than 100000 times the vibration frequency of the wave.

Preferably, the frequency fi is lower than 10Hz.

According to one embodiment, each disturbance PSi has the same amplitude for all electrical angles.

According to one embodiment, each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to standard servo control of the sensor and an estimated disturbance-compensated excitation force Fepi, and wherein the amplitude of the disturbance is selected such that the amplitude of the force Fepi is at least 10 times the amplitude of the force Fec.

The invention also relates to a method for measuring the angular velocity of a carrier on which the inertial sensor is arranged, the method comprising:

a phase of calibrating the inertial sensor implementing the calibration method as claimed in one of claims 1 to 9, said calibration phase being carried out upon activation of the inertial sensor,

step D of operating the inertial sensor, wherein the stored matrix is applied

And->

Before transmitting on the excitation transducer, the estimated inverse excitation matrix is +. >

Applied to the excitation force determined by said servo control, thereby pre-compensating said excitation force and +_ said estimated inverse detection matrix>

Is applied to the detected motion value to correct the detected motion value.

According to a variant, the method for measuring the angular velocity of a carrier on which the inertial sensor is arranged comprises:

a phase of calibrating the inertial sensor implementing the calibration method as claimed in one of claims 1 to 9, said calibration phase being carried out while the sensor is operating, then the measurement of the angular velocity being interrupted,

step D 'of measuring the angular velocity, step D' being performed during the calibration phase, is carried out by an additional inertial sensor also provided on the carrier,

step D of operating the inertial sensor, wherein the stored matrix is applied

And->

Before transmitting on the excitation transducer, the estimated inverse excitation matrix is +.>

Is applied to the detected motion value to correct the detected motion value.

The invention also relates to an inertial angle sensor comprising:

a resonator having a planar structure symmetrical about two perpendicular axes x and y, a sensor reference frame xy being defined between the two perpendicular axes x and y, and comprising two vibrating moving masses arranged around each other and configured to vibrate at a vibration frequency and in anti-phase in a direction x 'defining a wave reference frame x' y ', a vibration wave (OV) along x' forming an electrical angle (θ) with respect to the axis x,

a pair of excitation transducers to which excitation forces are applied along x and y, respectively, via a plurality of excitation controls, so as to maintain a desired form of vibration wave and vibrate along x'; and a pair of detection transducers configured to detect movement of the vibration waves along x and y,

a pair of transducers for compensating for the quadrature bias, the transducers for compensating for the quadrature bias being controlled via quadrature control CTxy; and a pair of frequency-tuned transducers controlled via frequency control CTx along x and frequency control CTy along y, respectively, the three controls CTx, CTy and CTxy being referred to as indexed fine tuning controls CTi, where i = 1, 2, 3,

The excitation control is determined by the servo control based on the detected motion, the sensor operates according to a gyroscopic tester mode,

for at least two electrical angles (thetaj) of the vibration wave, the three fine tuning controls CTi are configured to sequentially apply a sinusoidal stiffness disturbance PSi having a disturbance frequency fi,

a processing unit configured to:

based on the excitation control determined by the servo control, an estimated excitation force Fei to be applied to the resonator in the presence of said disturbance PSi is determined and stored,

based on the three estimated excitation forces fei=1, 2, 3 stored in the previous step, three 2 x 2 matrices M 'i are determined as a function of the electrical angle and the applied disturbance, the matrices M' i representing the response of the gyroscopic tester to the disturbance PSi,

determining and storing an estimated inverse excitation matrix based on the three matrices M' i determined in the previous step

And an estimated inverse detection matrix->

The excitation matrix E and the detection matrix D represent the effect of the excitation chain and the effect of the detection chain of the sensor respectively,

up to the excitation transducerBefore transmission, the estimated inverse excitation matrix

Is intended to be applied to an excitation force determined by said servo control, whereby said excitation force is pre-compensated, and said estimated inverse detection matrix +_ when the sensor is in operation >

Is intended to be applied to the detected motion value to correct said detected motion value.

The following description presents a number of examples of embodiments of the apparatus of the present invention: these examples do not limit the scope of the invention. These examples of embodiments contain not only the essential features of the invention, but also additional features related to the embodiments in question.

Drawings

The invention will be better understood and other features, objects and advantages thereof will become apparent from the following detailed description, given by way of non-limiting example, with reference to the accompanying drawings, in which:

fig. 1, which has already been mentioned, shows a MEMS sensor consisting of two vibrating moving masses arranged around each other.

Fig. 2, which has already been mentioned, shows the structure of a MEMS sensor with resonators symmetrical about two axes x and y defining the sensor reference frame.

Fig. 3, which has already been mentioned, shows a MEMS sensor with transducers on two masses.

Fig. 4, which has already been mentioned, illustrates the operation of an inertial sensor according to the prior art.

Fig. 5, which has already been mentioned, shows the effect of the excitation matrix on the values estimated by the servo control, and the effect of the detection matrix on the motion of the vibration wave.

Fig. 6 the effects of the excitation and detection chains are shown with dotted and solid lines, respectively, in fig. 6 already mentioned.

Fig. 7 already mentioned shows the ideal correction in excitation and detection.

Fig. 8 already mentioned shows the operation of the ideal correction of the sensor.

FIG. 9]Fig. 9 shows an estimated and thus imperfect inverse excitation matrix determined by the method according to the invention

Is applied to the substrate.

[ FIG. 10 ]]Fig. 10 shows an estimated and thus imperfect inverse detection matrix determined by the method according to the invention

Is applied to the substrate. />

Fig. 11 shows a method for calibrating a sensor according to the invention.

Fig. 12 shows an inertial angle sensor 10 embodying a calibration method according to the present invention.

Fig. 13 shows a sensor in operation for performing calibration according to the present invention.

Detailed Description

The calibration method according to the invention is applied to an inertial angle sensor comprising a resonator Res and transducers Et, dt, TF and TQ controlled by excitation control (Et) and fine tuning control (TF, TQ) as described above. The vibration wave OV vibrates at the vibration frequency ω. The servo control of the excitation control is in operation when the inertial sensor is operating in gyro-test mode, applying the method according to the invention.

The object of the invention is a calibration method that allows to determine an estimated inverse excitation matrix

And an estimated inverse detection matrix->

So as to improve the operation of the sensor by minimizing excitation and detection errors.

For this purpose, rather than on the excitation control (as in document US 9927256), the disturbance is sent via a fine tuning control. In normal operation of a gyroscope comprising three additional transducers (which are not discussed in the above cited documents), these controls have a completely different effect than the excitation control explained above.

Hereinafter, the fine tuning controls CTx, CTy, and CTxy are referred to as CTi, i=1, 2, 3, that is, CT1 for CTx, CT2 for CTy, and CT3 for CTxy, respectively.

This involves directly modifying the coefficients of differential equation (2) by inserting a new stiffness matrix Ktp by sending sinusoidal disturbances via these fine tuning controls CTi, without modifying the right hand side thereof (i.e. the applied excitation force as described in the cited document). It should be noted that the resonator is modified with a trimming comb and its displacement is constrained with excitation control.

As shown in fig. 9 for excitation and in fig. 10 for detection, an estimated matrix determined by the method according to the invention

And->

Are not ideal, that is, they are not exactly equal to the inverse of matrix E and the inverse of matrix D, respectively: although closer thereto, the product +.>

And->

Not equal to the identity matrix.

As shown in fig. 11, a method 100 according to the present invention includes: a first step A: for at least two electrical angles θj of the vibration wave, a sub-step A1 of sequentially applying a sinusoidal stiffness disturbance PSi of the disturbance frequency fi via each of the three fine tuning controls CTi is performed.

For this purpose, a sinusoidal voltage of frequency fi is applied to the control CTi.

For each applied disturbance PSi, based on the excitation control determined by the servo control, during sub-step A11, an estimated excitation force Fei to be applied to the resonator in the presence of said disturbance PSi in order to maintain the linear vibration is determined and stored. The characteristics of the resonator are changed by making them sinusoidal and observing the force that needs to be applied to have a linear wave.

The sinusoidal stiffness disturbance PS1 applied via control CT1 produces a change in sinusoidal stiffness of Kx corresponding to stiffness matrix Ktp 1:

the sinusoidal stiffness disturbance PS2 applied via control CT2 produces a change in sinusoidal stiffness corresponding to Ky of stiffness matrix Ktp 2:

The sinusoidal stiffness perturbation PS3 applied via control CT3 produces a change in the sinusoidal stiffness of Kxy corresponding to stiffness matrix Ktp 3:

then, during step B, three 2 x 2 matrices M 'i representing the gyroscope's response to the disturbance Psi are determined as a function of the electrical angle θj and the applied disturbance Psi, based on the three estimated excitation forces fei=1, 2, 3 stored in step a 11. Preferred modes of computation of matrix M' i are described further below.

Finally, in step C, an estimated inverse excitation matrix is determined and stored based on the three matrices M' i determined in step B

And an estimated inverse detection matrix->

Once these estimated matrices have been determined and stored, they are intended to be implemented during the operation of the sensor, that is to say when the sensor performs measurements: before being transmitted over the excitation transducer,

to be applied to the excitation forces determined by the servo control, so as to pre-compensate these excitation forces; />

Is intended to be applied to the detected motion values to correct them. Thus, the measured excitation and detection errors are minimized by applying the estimated inverse matrix.

In other words, with the complementary actuators included in certain MEMS gyroscopic testers that provide complementary observability, the method according to the present invention has the benefit of "easily" determining the detection and excitation faults through calculation.

In fact, according to one embodiment, the method according to the invention is iterative, thus allowing to increase its precision. Typically, no more than two iterations.

When the above-described disturbance matrix Ktpi is applied to the transducers TQ and TF, for the first variant in which only the disturbance PSi is applied and no conventional fine tuning control is applied (in which case the fine tuning servo control is inoperable), equation (2) becomes:

fi, denoted as two components (FX, FY), is referred to as the applied excitation force for simplicity. Fi is decomposed into a standard excitation force Fc (FXc, FYc) for performing the current servo control of the sensor in the absence of disturbances, and a compensation excitation force Fpi (FXpi, FYpi) for compensating the application of disturbances PSi:

it can be seen that the application of the perturbation brings about a modification of some of the coefficients in differential equation (5) relative to conventional equation (2):

Fi＝Fc+Fpi；FXi＝FXc+FXpi；FYi＝FYc+FYpi

the amplitude of the applied disturbance PSi is chosen such that the amplitude of (FXpi, FYpi) is at least 10 times the amplitude of (FXc, FYc). This selection is made so that the phenomenon to be observed easily emerges from noise and is more easily observed. However, the amplitude cannot be increased too much, since the control does not actually allow this to occur.

The force Fc controls the resonator in a conventional manner such that the wave (for example) is linear and of a given amplitude, and results (in a similar manner to equation (1):

due to the frequency difference between Fc and Fp, it is possible to separate out due to the linearity of the system:

according to a second variant, the disturbance PSi is applied superimposed on the conventional fine control (matrix Kt) (fine servo control then in operation). Equation (2) then becomes:

likewise, the conventional servo control of the resonator is expressed as:

and equation (7) still proves to be correct.

Based on equations (7) and (3) and (4), excitation matrix E and detection matrix D (which are also referred to as excitation error matrix and detection error matrix) are introduced:

wherein Fe (FXe, FYe): the estimated forces for controlling the oscillator are decomposed into forces Fec (FXec, FYec) and Fepi (FXepi, FYepi) according to the same logic as described above:

fec: a standard excitation force for performing an estimation of a conventional servo control of the sensor in the absence of disturbances,

fepi: an estimated compensating excitation force for compensating for the application of the disturbance.

Namely fxei=fxec+fxepi and fyii=fyiec+fyiepi

The actual applied force has the following values:

based on

Extracting->

Is a function of the amplitude of (a).

FXec and fysec are sinusoidal functions of frequency ω.

FXepi and FYepi are sinusoidal functions of ω, which are modulated by the disturbance introduced in Ktpi (i.e. at frequency fi).

Theoretically, it is obtained:

because by definition->

Is the force that counteracts the disturbance.

For each trimming comb and thus each applied disturbance PSi, and for the vibration angle θ of the wave, it is theoretically obtained:

/>

wherein:

x0 is the known amplitude of the vibration controlled by servo control

Omega is the known angular frequency of the resonator

Ai is the known amplitude of the disturbance PSi

fi is the known frequency of the disturbance PSi

θ is the known angle to which the gyroscopic tester is controlled

For i=1, the calculation is performed, and for i=2 and 3, the reason is the same.

The magnitudes of the terms to the right and left of equation (9) are the same, and thus theoretically result in:

wherein AFXep1 (θ) represents the magnitude of FXep1 (θ).

It is desirable to determine

In order to derive therefrom a matrix M'1 as defined below:

wherein the method comprises the steps of

The forces Fei (FXei, FYei) stored in step a11 are provided, that is to say in this case:

is sinusoidal at the angular frequency omega of the resonator,

is a sine modulated by a sine function at an angular frequency 2 pi f1 at the angular frequency ω of the resonator.

Demodulation is performed in ω and then in 2pi.f1 to determine

Is obtained by the amplitude of (a)

(demodulation is an operation well known to those skilled in the respective arts).

Thus, according to one embodiment of the invention, step B comprises:

substep B1, demodulating each estimated excitation force Fei with the vibration frequency ω and then with the associated disturbance frequency fi, to obtain the amplitude AFpei (AFXpei, AFYpei) of the disturbance compensated excitation force Fepi (FXepi, FYepi).

Substep B2, determining the matrix M' i based on the magnitude of the force Fepi determined in B1.

According to one embodiment of the invention, each matrix M 'i representing the response of the gyroscopic tester to the disturbance M' i and determined in step B has the following form:

wherein mi=1, 2, 3 is defined by:

and->

/>

How to determine M' i based on AFpei will now be explained.

We start from equation (12):

it may be of the form:

a1, X0, θ, AFXep1 (θ) and AFYep1 (θ) are known.

M'1 has 4 unknowns (4 coefficients). Therefore, at least two angles are required to obtain the four coefficients of M' 1.

In fact, this process is performed for more than two angles, and statistical filtering, typically of the least squares type, is performed to best estimate the coefficients of M' 1. Thus, according to one embodiment, step a is performed with a plurality of electrical angles, and then the matrix M' i is determined in step B by statistical filtering minimization (e.g. of the least squares type) of the contribution of the noise of the sensor.

Thus, based on equation (14) and the respective known quantities, a basis is provided

Estimated M'1, namely:

the same procedure is performed for M '2 and M' 3.

It will now prove possible to determine by means of equations (15) to (17) based on the matrix M' i determined in step B (using equation (14) and its equivalent for i=2 and 3)

And->

This is a nonlinear problem, but because the electronic error is small

And->

Is a matrix close to the identity matrix.

Thus, it is possible to decompose them:

where I represents an identity matrix and eij, dij are smaller values (typically less than 0.01)

Thus:

the second order term is ignored.

Based on AMi +mib=known M' i, it will be possible to determine a and B.

For M1:

d12 and e21, and e11+d11 are thus identified.

For M2:

d21, e12 and e22+d22 are obtained.

For M3:

thus e22+d11 and e11+d22 are obtained, which allows to combine with e11+d11 from (20) and e22+d22 from (21).

It should be noted that equations e22+d11, e11+d22, e11+d11 and e22+d22 are not independent, the system has rank 3: for example, (e22+d22) + (e11+d11) - (e11+d22) =e22+d11. Therefore, it is impossible to determine 4 coefficients from 4 equations. But the right and left sides of equation (8) can be arbitrarily multiplied by any value. For example, it is possible to arbitrarily decide to divide a cut value by (1+d11) so that in the new system, d11 will be equal to 0, thereby eliminating the unknowns, and so that it is possible to determine the unknowns e22, then determine d22, then determine e11.

Thus, according to one embodiment of the method according to the invention, the three representative matrices M ' i determined in step B (ignoring the second order term) are represented in the form of M ' i= AMi +mib, and step C comprises the sub-step of determining the matrices a and B (8 coefficients) based on said matrices M ' i. Thus, using the claimed method, all 8 coefficients are observable. The matrix is then determined based on A and B (equations (18) and (19))

And->

By simulating the actual behavior of the gyroscopic tester in detail, it is possible to determine the coefficients of the simulation of the matrices E and D. When using these simulated coefficients and determined according to the method of the invention

And->

Calculated amount of coefficient of (2)>

And->

When an identity matrix with an error between 10ppm and 200ppm is obtained, this constitutes a pair

And->

Is a very high precision estimate of (1).

In order to make the stiffness change in equation (8) slow enough to be considered constant, it is preferable to select frequencies f1, f2 and f3 of the disturbances PS1, PS2 and PS3 much lower than the vibration frequency ω, which typically lie between less than 1000 times and less than 100000 times. Since the vibration frequency of the wave is typically on the order of about ten kHz, the frequencies f1, f2 and f3 are typically below 10Hz or even below one Hz.

Furthermore, the frequencies f1, f2 and f3 of the disturbances PS1, PS2 and PS3 are preferably chosen to be greater than the frequency of the physical phenomena responsible for the drift of the sensor or more specifically of the physical phenomena related to the variation of the temperature of the sensor. These phenomena typically have frequencies much lower than one Hz or even one tenth Hz.

Therefore, the frequencies f1, f2 and f3 are preferably greater than 0.1Hz.

Preferably, frequencies f1, f2 and f3 are injected separately; these frequencies may be equal. However, this is not important for the implementation of the method.

Fig. 12 shows an inertial angle sensor 10 implementing a calibration method 100 according to the present invention. The disturbance PSi is applied to the transducers TQ or TF in turn. The processing unit UT effects a change of the reference frame on the resulting estimated motion (Xe, ye) of the vibrations and then calculates an estimated excitation control allowing servo control of the sensor in the presence of disturbances (servo control module Ass). Then, after returning to the sensor reference frame, the (MEM) estimated excitation forces FXei, FYei are determined and stored. Based on these forces, the processing unit determines a matrix

And->

And store them.

FIG. 13 shows the sensor in operation, that is to say during the execution of the measurement of the angular velocity, the calibration has ended and the matrix

And->

Is stored. The processing unit will->

Applied to the motion measured by the sensor and will +.>

To the excitation force estimated by the servo control. The fine servo control (not shown) then operates in a conventional manner.

The calibration method may be implemented according to a plurality of usage modes.

For all modes, once calibration has been achieved and when the sensor is in operation, the estimated inverse excitation matrix is applied before transmission on the excitation transducer

Applied to the excitation force determined by the servo control, thereby pre-compensating said excitation force and inverting the estimated detection matrix +.>

Applied to the detected motion value, thereby correcting the detected motion value.

In a first mode of use, the phase of calibrating the inertial sensor implementing the method 100 according to the invention is performed, typically at the output of a manufacturing chain (factory calibration), before the sensor is put into operation. The inverse excitation and detection matrix is stored in the processing unit. The inverse excitation and detection matrix is then applied while the sensor is in operation and is performing measurements.

According to a second mode of use, the invention relates to a method for measuring the angular velocity of a carrier on which an inertial sensor 10 is arranged, comprising implementing a calibration method according to the invention 100 and a calibration phase implemented when the sensor is activated. Once the calibration has ended, step D involves performing the application of the stored matrix

And->

Is a measurement of (a).

According to a third mode of use, the invention relates to a method for measuring the angular velocity of a carrier on which an inertial sensor 10 is arranged, comprising a calibration phase implementing the calibration method 100 according to the invention and realized during operation. In the calibration phase, the inertial sensor cannot perform the measurement and, therefore, the measurement of the angular velocity by the sensor 10 is interrupted during the calibration phase.

When calibration of the sensor 10 is being performed, the method carries out a step D' of measuring the angular velocity, which is performed by an additional inertial sensor also provided on the carrier, and this step is done in order to ensure continuity of the measurement.

Once the calibration has ended, the sensor 10 is calibrated by applying the stored matrix in step D

And->

To re-establish control of the measurement.

For example, switching from one sensor to another is effected periodically in time, allowing calibration throughout the duration of operation of the sensor 10.

By simulating the actual behavior of the gyroscopic tester in detail, it is possible to determine the coefficients of the simulation of the matrices E and D.

Determined when using the method according to the invention

And->

Calculated amount of coefficient of (2)>

And

an identity matrix with an error between 10ppm and 200ppm is obtained, which is a very high accuracy. />

Claims

1. A method (100) for calibrating an inertial angle sensor (10), the inertial sensor comprising:

a resonator (Res) having a planar structure symmetrical about two perpendicular axes x and y between which a sensor reference frame xy is defined, and comprising two vibrating moving masses (M1 and M2) arranged around each other and configured to vibrate in anti-phase at a vibration frequency (ω) and in a direction x 'defining a wave reference frame x' y ', a vibration wave (OV) along x' forming an electrical angle (θ) with respect to said axis x,

a pair of detection transducers (Dt) configured to detect movement of the vibration waves along x and y; and a pair of excitation transducers (Et) to which excitation forces are applied in x and y, respectively, via a plurality of excitation controls determined by servo control based on the detected motion, and for maintaining the vibration wave in a desired form and vibrating in x', an

A pair of Transducers (TQ) for compensating for quadrature bias, said transducers being controlled via quadrature control CTxy, and a pair of frequency-adjusting Transducers (TF), said frequency-adjusting transducers being controlled via frequency control CTx along x and frequency control CTy along y, respectively, said three controls CTx, CTy and CTxy being referred to as fine tuning control CTi indexed by i, wherein i = 1, 2, 3,

the method is applied while the sensor is operating according to a gyroscopic tester mode, and comprises the steps of:

a, at least two electrical angles (θj) for said vibration wave:

a1, sequentially applying a sinusoidal stiffness disturbance PSi having a disturbance frequency fi via each of the three fine tuning controls CTi, and for each applied disturbance:

a11, based on the excitation control determined by the servo control, determining and storing an estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi,

b, determining three 2 x 2 matrices M 'i as a function of said electrical angle and said applied disturbance, the matrix M' i representing the response of said gyroscopic tester to said disturbance PSi,

And an estimated inverse detection matrix->

Excitation matrix E and detection matrix D represent the effect of the excitation chain and the effect of the detection chain, respectively, of the sensor.

2. The method of claim 1, wherein each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec and an estimated disturbance-compensated excitation force Fepi corresponding to standard servo control of the sensor,

and wherein step B comprises the sub-steps of:

b1) demodulating each estimated excitation force Fei with said vibration frequency (ω) and then with the associated disturbance frequency fi to obtain an amplitude (AFpei) of said disturbance compensated excitation force Fepi,

b2, determining the matrix M' i based on the magnitude of the force Fepi.

3. A method according to any one of the preceding claims, wherein step a is performed with a plurality of electrical angles, and then the matrix M' i is determined in step B by statistically filtering the contribution of noise of the sensor to be minimized.

4. The method according to one of the preceding claims, wherein each representative matrix M' i determined in step B has the form:

Mi is defined by:

and +.>

5. Method according to the preceding claim, wherein the matrix

And->

Is considered to be close to the unitary matrix and is expressed as:

M’i＝AMi+MiB

6. The method according to one of the preceding claims, wherein the disturbance frequency fii = 1, 2, 3 is between 1000 times less than the vibration frequency (ω) of the wave and 100000 times less than the vibration frequency (ω) of the wave.

7. The method according to one of the preceding claims, wherein the frequency fi is below 10Hz.

8. Method according to one of the preceding claims, wherein each disturbance PSi has the same amplitude for all the electrical angles.

9. Method according to one of the preceding claims, wherein each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to standard servo control of the sensor and an estimated disturbance compensation excitation force Fepi, and wherein the amplitude of the disturbance is selected such that the amplitude of the force Fepi is at least 10 times the amplitude of the force Fec.

10. A method for measuring an angular velocity of a carrier on which an inertial sensor (10) is arranged, the method comprising:

stage of calibrating the inertial sensor implementing the calibration method (100) according to one of claims 1 to 9, the calibration stage being implemented when the inertial sensor is activated,

step D of operating the inertial sensor, wherein the stored matrix is applied

And->

Before transmitting on the excitation transducer, the estimated inverse excitation matrix +.>

To the excitation force determined by the servo control, thereby pre-compensating the excitation force, and inverting the estimated detection matrix +.>

Is applied to the detected motion value to correct the detected motion value.

11. A method for measuring an angular velocity of a carrier on which an inertial sensor (10) is arranged, the method comprising:

stage of calibrating the inertial sensor implementing the calibration method (100) according to one of claims 1 to 9, the calibration stage being carried out while the sensor is operating, then the measurement of the angular velocity being interrupted,

a step D 'of measuring said angular velocity, said step D' being performed during said calibration phase, implemented by an additional inertial sensor also provided on said carrier,

Step D of operating the inertial sensor, wherein the stored matrix is applied

And->

Is applied to the detected motion value to correct the detected motion value.

12. An inertial angle sensor (10), comprising:

A pair of excitation transducers (Et) to which excitation forces are applied along x and y, respectively, via a plurality of excitation controls, so as to maintain the vibration wave in a desired form and vibrate along x'; and a pair of detection transducers (Dt) configured to detect movement of the vibration waves along x and y,

a pair of Transducers (TQ) for compensating for quadrature bias, said transducers for compensating for quadrature bias being controlled via quadrature control CTxy; and a pair of frequency-tuned Transducers (TF) controlled via frequency control CTx along x and frequency control CTy along y, respectively, the three controls CTx, CTy and CTxy being referred to as indexed fine tuning controls CTi, where i = 1, 2, 3,

the excitation control is determined by servo control based on the detected motion, the sensor operates according to a gyroscopic tester mode,

for at least two electrical angles (θj) of the vibration wave, the three fine tuning controls CTi are configured to sequentially apply a sinusoidal stiffness disturbance PSi having a disturbance frequency fi,

a processing Unit (UT), the processing unit configured to:

for each applied disturbance, determining and storing an estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi based on the excitation control determined by the servo control,

Based on the three estimated excitation forces feii=1, 2, 3 stored in the previous step, three 2 x 2 matrices M 'i are determined as a function of the electrical angle and the applied disturbance, the matrices M' i representing the response of the gyroscopic tester to the disturbance PSi,

And an estimated inverse detection matrix->

Excitation matrix E and detection matrix D represent the effect of the excitation chain and the effect of the detection chain of the sensor respectively,

the estimated inverse excitation matrix prior to transmission on the excitation transducer

Is intended to be applied to the excitation force determined by the servo control, thereby pre-compensating the excitation force, andand when the sensor is in operation the estimated inverse detection matrix +.>

Is intended to be applied to the detected motion value to correct said detected motion value. />